How to model a vase with a hole through it?
Ignore the hole to begin with. The main shape appears to be a squashed cylinder, so create the main outline by scaling down one axis, then loop cutting/extruding and scaling to create the overall shape. For the neck the shape is circular so un-squash this section. For the large hole, boolean a cylinder then clean up the geometry afterwards.


Start with a 16 sided cylinder. I used a 100mm rad and 350mm height. Scale it down on one axis. Add loop cuts.

From bottom ring to top I scaled by about .7, .9, 1, .9, .6, .1, .1. Rounded the neck rings. Added supporting loops for the neck and base. Inset and extruded the neck downward. Delete end N-Gons then used Grid Fill to finish.

Add a 10 sided cylinder and shape accordingly. I am trying to end up with an easy way to create quads after the boolean so am looking to position the new cylinder vertices close to the vase vertices.

Snap and merge the resulting vertices together, creating quads. Tidy up the mesh. At this step I deleted half the model and mirrored the mesh to save time. Remember to flip normals on the mirror. Add supporting loops to the inner ring.

Subdivision result. This worked out better than my first attempt as there are now no triangles in the bottom corners of the hole.